Weekly Problem 3 - 2016

How many times has Simon's age changed from a square to a prime?

Weekly Problem 45 - 2013

Which of the numbers shown is the product of exactly 3 distinct prime factors?

Weekly Problem 25 - 2011

Each time a class lines up in different sized groups, a different number of people are left over. How large can the class be?

Weekly Problem 45 - 2009

Flora has roses in three colours. What is the greatest number of identical bunches she can make, using all the flowers?

Weekly Problem 49 - 2013

What is the value of 2000 + 1999 × 2000?

Weekly Problem 5 - 2007,br />hen coins are put into piles of six 3 remain and in piles of eight 7 remain. How many remain when they are put into piles of 24?

Weekly Problem 52 - 2009

Gar the Magician plays a card trick on his friends Kan and Roo. Can you work out his trick and find out the sum on Kan's cards?

Weekly Problem 19 - 2012

The diagram shows a large rectangle composed of 9 smaller rectangles. If each of these rectangles has integer sides, what could the area of the large rectangle be?

Weekly Problem 11 - 2009

How many of the numbers 1 to 20 are not the sum of two primes?

Weekly Problem 21 - 2013

In how many ways can seven of the numbers 1-9 be chosen such that they add up to a multiple of 3?

Weekly Problem 1 - 2016

What is the last-but-one digit of 99! ?

Weekly Problem 17 - 2010

The value of the factorial $n!$ is written in a different way. Can you work what $n$ must be?

Weekly Problem 41 - 2006

Helen buys some cakes and some buns for her party. Can you work out how many of each she buys?

Weekly Problem 2 - 2016

How many tables of each type does Mark need at his birthday party?

Weekly Problem 22 - 2010

Can you form this 2010-digit number...

Weekly Problem 35 - 2006

A number has exactly eight factors, two of which are 21 and 35. What is the number?

Weekly Problem 41 - 2009

At a cinema a child's ticket costs £$4.20$ and an adult's ticket costs £$7.70$. How much did is cost this group of adults and children to see a film?

Weekly Problem 37 - 2006

What digit must replace the star to make the number a nultiple of 11?

Weekly Problem 35 - 2011

You are given lots of clues about a number. Can you work out what it is?

Weekly Problem 7 - 2016

What is the smallest number of pieces grandma should cut her cake into to guarentee each grandchild gets the same amount of cake and none is left over.

Weekly Problem 38 - 2010

The product of four different positive integers is 100. What is the sum of these four integers?

Weekly Problem 24 - 2006

How many of the rearrangements of the digits 1, 3 and 5 give prime numbers?

Weekly Problem 1 - 2009

Our school dinners offer the same choice each day, and each day I try a new option. How long will it be before I eat the same meal again?

Weekly Problem 6 - 2010

Can you find three primes such that their product is exactly five times their sum? Do you think you have found all possibilities?

Weekly Problem 25 - 2006

Chocolate bars come in boxes of 5 or boxes of 12. How many boxes do you need to have exactly 2005 chocolate bars?

Weekly Problem 4 - 2009

Bilbo and Frodo use a rhyme as they count their own cherry stones - where will they finish if they count all stones together?

Weekly Problem 7 - 2010

Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?

Weekly Problem 48 - 2013

What is the remainder when the number 743589×301647 is divided by 5?

Weekly Problem 41 - 2008

How many pairs of numbers of the form $x$, $2x+1$ are there in which both numbers are prime numbers less than $100$?

Weekly Problem 48 - 2010

Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?

Weekly Problem 5 - 2011

Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?

Weekly Problem 10 - 2008

If the numbers 1 to 10 are all multiplied together, how many zeros are at the end of the answer?

Weekly Problem 26 - 2014

Which of the given numbers are divisible by 6?

Weekly Problem 12 - 2008

A male punky fish has 9 stripes and a female punky fish has 8 stripes. I count 86 stripes on the fish in my tank. What is the ratio of male fish to female fish?

Weekly Problem 22 - 2008

The following sequence continues indefinitely... Which of these integers is a multiple of 81?

Weekly Problem 39 - 2014

A whole number less than 100 gives remainders of 2, 3 and 4 when divided by 3, 4 and 5. What is the remainder when it is divided by 7?

Weekly Problem 26 - 2008

If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?

Weekly Problem 30 - 2010

Find out which two distinct primes less than $7$ will give the largest highest common factor of these two expressions.

Weekly Problem 1 - 2015

If $p$ and $q$ are prime numbers greater than $3$ and $q=p+2$, prove that $pq+1$ is divisible by $36$.

Weekly Problem 4 - 2015

Given any positive integer n, Paul adds together the factors of n, apart from n itself. Which of the numbers 1, 3, 5, 7 and 9 can never be Paul's answer?

Weekly Problem 5 - 2014

What is the sum of the digits of the largest 4-digit palindromic number which is divisible by 15?

Weekly Problem 32 - 2007

One of these numbers is the largest of nine consecutive positive integers whose sum is a perfect square. Which one is it?

Weekly Problem 6 - 2015

Charlie doesn't want his new house number to be divisible by 3 or 5. How many choices of house does he have?

Weekly Problem 15 - 2014

How many three digit numbers formed with three different digits from 0, 1, 2, 3 and 5 are divisible by 6?

Weekly Problem 33 - 2015

How many integers $n$ are there for which $n$ and $n^3+3$ are both prime?

Weekly Problem 32 - 2006

How many zeros are there at the end of $3^4 \times 4^5 \times 5^6$?

Weekly Problem 7 - 2011

Roo wants to puts stickers on the cuboid he has made from little cubes. Will he have any stickers left over?

Weekly Problem 13 - 2009

How many zeros does 50! have at the end?

Weekly Problem 28 - 2014

What is the units digit of the given expression?

Weekly Problem 10 - 2011

Will this product give a perfect square?